On the tidal spin up and orbital circularization rate for the massive X-ray binary systems

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Abstract
We calculate the response of non-rotating main-sequence stars of 5, 10 and 20 solar masses to a periodic perturbing tidal potential. The fully non-adiabatic, but linearized, equations for the response are solved numerically. Our results enable the spin up and orbital circularization rates to be calculated for a wide range of orbital frequencies. We discuss the behaviour of these quantities for orbital parameters appropriate to the massive X-ray binaries. The spin up of the massive component appears to be rather inefficient in our calculations, unless the system could be locked into resonance. However, because the tidal torque is strongly concentrated in the outer layers these may be spun up (or for certain orbital frequencies spun down) much more efficiently. We expect a complicated state of rotation to be set up in the massive component. When the orbital eccentricity is small the final orbital circularization can be very effective when the system passes through a resonance.

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